Given:
Word: EXAMINATION
Total letters = 11
Frequency of letters:
A = 2, I = 2, N = 2
E = 1, X = 1, M = 1, T = 1, O = 1
Step 1: Identify letters before E
In dictionary order, the only letter before E is A.
So, we count the number of permutations that start with A.
Step 2: Fix A at the first position
After fixing one A at the first position, remaining letters are:
A = 1, I = 2, N = 2
E = 1, X = 1, M = 1, T = 1, O = 1
Total remaining letters = 10
Step 3: Count distinct permutations
Number of distinct permutations:
= 10! / (2! × 2!)
= 3628800 / 4
= 907200
Final Answer:
Number of words before the first word starting with E = 907200